Does anyone know how to restore it?
What do you mean by objectives? Job goal, school, or Zoi ambitions?
Job and school “To Dos”
Zoi has work and school options on her phone clicking on either one will show them to you.
Hi! A reminder that if somebody solved your issue you can mark the message as a solution so that other people will see it above and don’t have to scroll down 
Did it disappear after pressing a key by any chance? If so, try pressing O, as that can toggle the Objectives panel.
If that doesn’t bring it back, could you share a screenshot of your screen? That will help narrow down whether it’s just the UI that’s hidden or if something else is going on.